Defining parameters
Level: | \( N \) | \(=\) | \( 10000 = 2^{4} \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 10000.cc (of order \(100\) and degree \(40\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 500 \) |
Character field: | \(\Q(\zeta_{100})\) | ||
Sturm bound: | \(3000\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(10000, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 61200 | 9000 | 52200 |
Cusp forms | 58800 | 9000 | 49800 |
Eisenstein series | 2400 | 0 | 2400 |
Decomposition of \(S_{2}^{\mathrm{new}}(10000, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(10000, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(10000, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(500, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1000, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2000, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2500, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(5000, [\chi])\)\(^{\oplus 2}\)